Question

Choose the slope-intercept equation of the line that passes through the point (6, -6) and is perpendicular to y = 3x - 6.
y = 1/3x - 8
y = -3x + 12
y = 3x - 24
y = -1/3x - 4

Answer 1

ok so first of all if your linear equation need to be perpendicular to another linear equation you automatically know that their slopes maintains:

\[Y _{1} = a*X _{1} + b , Y _{2} = c*X _{2} + d ==> a=-c ^{-1} / c =- a ^{-1}\]

in your case if c=3 then a has to be -1/3 , with your answers you can know now that the correct answer is "d" but how did they get to the -4 there?

we also know that to calculate a slop of a linear equation we have the next formula : \[\frac{ Y _{1}-Y _{2} }{ X _{1}-X _{2} } = a\]

and also the b is the point the our equation is touching the Y axis so we know our line is going through the point (0,b) -->

\[\frac{ b-(-6) }{ 0-6 } = -1/3 ==> b+6 = 2 ==> b=-4\]

Answer 2

*"b is the point Where our..."